WBJEE · Maths · Indefinite Integration
\(\int \sqrt{1+\cos x} d x\) is equal to
- A \(2 \sqrt{2} \cos \frac{\mathrm{x}}{2}+\mathrm{C}\)
- B \(2 \sqrt{2} \sin \frac{\mathrm{x}}{2}+\mathrm{C}\)
- C \(\sqrt{2} \cos \frac{x}{2}+C\)
- D \(\sqrt{2} \sin \frac{x}{2}+C\)
Answer & Solution
Correct Answer
(B) \(2 \sqrt{2} \sin \frac{\mathrm{x}}{2}+\mathrm{C}\)
Step-by-step Solution
Detailed explanation
Hints: \(\int \sqrt{1+\cos x} d x=\sqrt{2} \int \cos \left(\frac{x}{2}\right) d x=2 \sqrt{2} \sin \left(\frac{x}{2}\right)+c\)
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